I am designing a billboard with artwork that is 12" x 24" with a resolution of 500. (This is what they wanted.) The psd file is 170MB and they only want a 20MB file. I am using Photoshop CC. How do I save this file as a PDF that's about 20MB without compromising the quality? I am a complete beginner. Thanks
Depending on your colour depth, 72 megapixels (12" x 24" @ 500 PPI) will not quite get to a 20MB file with a lossless compression. So you will probably have to comprise the quality somewhat. You can do this in a way that might not be noticeable.
I would check how far JPEG2000 would get me and go from there. Don't forget that this file size is just a guide line, the printer will likely accept the file if it is close enough.
The 'proper' way would be to look at your image and decide which compression technique fits best. For example if you have an image with a lots of graphic design reducing the colour space to the most common colours might be a great idea. Or for a more photographic image you could loose some of the chrominance information by choosing for chroma subsampling.
Either way, I highly recommend going to the printer and see one print. It is amazing to see a print head flying past whilst splattering the canvas!